I am working a problem to find the GCF of 3 trinomials. I am having trouble fact

Question

I am working a problem to find the GCF of 3 trinomials. I am having trouble factoring one of them. The trinomial is:

[6x(3)-10x^(2)-4x]

I factored with 2x to get: [2x{3x^(2)-5x-2}]

Now I cant figure out how to factor {3x^(2)-5x-2}. From the other exercies i have practiced, you factor the -2 and see what factorings fit to equal 5. I cant figure out how this fits since for 2, the factors would be 2,1? The solution says (3x+1)(x-2) and doing the multiplication i see that it is correct, but i am not understanding how to get this?

Explanation / Answer

3x^2 - 5x - 2 = 0

x = [-(-5) +- SQRT(5^2 - 4(3)(-2)] / (2(3))

x = [5 +- SQRT(25 + 24)] / 6

x = (5 +- 7) / 6

x = 12/6 or x = -2/6

x = 2 or x = -1/3

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